In various methods for desulfurizing industrial gases, for example, the extracted sulfur is finely dispersed in an aqueous suspension and forms a sulfur paste. Elemental sulfur can be obtained from the paste by drying it; however much more energy can be saved, and greater economies practiced, by heating the paste until the sulfur melts, after which the water and sulfur phases are separated in a settling device as a result of their different densities. In order to prevent the water in the paste from evaporating when the sulfur melts (at approximately 113.degree. C.), the melting process must occur at a pressure of 2 to 5 bars in an autoclave. Sulfur-melting autoclaves of this type have been used in the past, but are limited to batch operations, meaning that the individual steps (i.e., pouring in, melting, phase separation and emptying) occur in succession rather than on a continuous basis.